Returning to Beijing Airport to catch a flight after first exit regarded as multi entry?

I have booked flight tickets for my daughter to depart from London on 9 May and return on 2 July 2015. However, as she is on a X type, she is not entitled to a multi entry one. She plans to leave around mid June to travel around South East Asia. Can she fly into Beijing Airport from wherever she is in Asia to catch her return flight to London? Is this acceptable to the Chinese authorities? In addition, can she apply for the 72 hour visa?